"Silence" was one of the first books I read after coming as a missionary to Japan five years ago. I have not yet watched the movie, but since it takes us awhile to see movies in Japan, I thought I would put in my two cents here while it still might be useful.
Below is a recap of the storyline so we're all on the same page in case the movie differs somewhat from the book (warning: if you haven't yet seen the movie or read the book, this might spoil some things for you). Following that, I have included an analysis of some of the key points in the book.
Two Portugese priests, Rodrigues and Garrpe, go to Japan in search of their former mentor (Ferreira) with whom all contact has been lost as the persecution of Christians has intensified. Rumours, that Ferreira has recanted his faith, have started to trickle out of Japan.
They decide to go to Japan, find their mentor and dispel the rumours, and also try to strengthen and encourage the Japanese Christians remaining in Japan. Along the way, they meet a Japanese man (Kichijiro) who agrees to guide them to Christians on their arrival. Rodrigues eventually begins to suspect that Kichijiro is himself a Christian, though he has a hard time believing that such a lazy, cowardly person could be one.
When they land in Japan, Kichijiro quickly connects Gaarpe and Rodrigues with some local Christians. The villagers hide the men and are very happy to have priests in their midst again. Gaarpe and Rodrigues minister to the villagers, but eventually the authorities are tipped off.
Two of the main village spiritual leaders are arrested, and are drowned by being tied to a post which is put into the ground at a beach. As they suffer, they sing. Their songs haunt Rodrigues. Shortly thereafter, the villagers ask Rodrigues and Gaarpe to leave because their presence now endangers everyone. Gaarpe and Rodrigues decide to split up.
Eventually Rodrigues and Kichijiro cross paths again. It is revealed that Kichijiro is himself a Christian, but has recanted. Kichijiro betrays Rodrigues to the authorities for a price, and saves his own skin by stepping on a fumie (an icon of Jesus or Mary) and recanting again.
The first prison that Rodrigues is taken to is almost too pleasant. There are other Christians there, and he is allowed to minister to them. He lives a life of relative ease, until one day he is told that if he doesn't apostatize the Christians will suffer because of him. He realizes that the ease he has experienced has been a ruse to try and break down his will; he imposes harsher sanctions on himself to try and build up a resistance to persecution. Rodrigues is then transferred to a different prison. Along the way, he notices that Kichijiro is following him, and the man keeps vigil outside of the new prison. At one point the guards notice him, and once more Kichijiro steps on a fumie to recant and prove that he's not a Christian.
At the new prison, Rodrigues is eventually brought before Inoue (the governor of Chikugo, and the architect of the persecution against the Christians). They have a few intellectual conversations. Eventually, Rodrigues is taken out to witness a scene. Gaarpe has been captured. Some of the Christians (with whom Rodrigues had bonded at his previous prison) are taken out in a boat and threatened with drowning, unless Gaarpe recants. Rodrigues calls out to him, encouraging him to recant. Gaarpe refuses; the Christians are thrown in the water wrapped in mats; and Gaarpe rushes into the water to try and save them, drowning himself too.
Next, Rodrigues is brought to Ferreia's house. The old mentor has indeed recanted, and encourages Rodrigues to do likewise. When he is returned to his prison, Rodrigues is told that he, too, will be tortured and killed the next day unless he recants. He is transferred to a much less comfortable place.
Through the night he prays. Eventually the absurdity of hearing a guard snoring as he goes through his "dark night of the soul" strikes him and he begins to laugh. Ferreira is brought in, and asks why he is laughing. Rodrigues references the "snoring", and Ferreira tells him that it is not snoring but the sounds of prisoners being tortured in a nearby pit. This, coupled with Ferreira's convincing arguments, eventually turns Rodrigues. The man hallucinates that the face of Jesus on the fumie is telling him to recant. He eventually does so.
From then on, like Ferreira, Rodrigues lives the life of a prisoner under house arrest. He is forced to marry, and is used as a consultant for the Japanese government when they find suspicious artifacts in Japanese houses (i.e., artifacts that might be Christian, and therefore would brand their owners as Christians and worthy of death). He lives out his days in this way, sometimes interacting with with his old acquaintance, Kichijiro. Rodrigues fills the role of priest to Kichijiro in their post-recantation exile.
Now for some thoughts and comments on "Silence".
Rodrigues goes to Japan in search of his old mentor (Fereria). That is the primary reason for his journey, as far as I can tell, with the secondary reason being to help strengthen the church.
We should take warning from this. Those who are missionaries must ask, "What has been our reason for coming as missionaries to any given place? Does it have its roots in earthly things, or is it God-ordained?" We need to root ourselves in our purpose and continually revisit it. We need to constantly fix our eyes on Jesus, and not allow worldly distractions or motives to entangle us.
Even "good" things can be distractions. Rodrigues says that his reason for being a priest is to "help people". The sufferings and deaths of the Christians—"Unless you recant," one of the persecutors said—would have had a profound impact on anyone. But because his cause was for people rather than God, was Rodrigues' resolve weakened?
Am I willing to have others die for my faith? I cannot answer. I would make the same decisions, but for the grace of God. I know my own feebleness, but as Rodrigues says, vanity is always insidiously present in the human soul.
To trample on an icon in my belief is not a sin. It is what this symbolizes—a denial—which is the sin.
What do we make of what the icon "said" to Rodrigues before he stepped on the fumie? (To quote the book, the icon says: "Trample! Trample! I more than anyone know of the pain in your foot. Trample! It was to be trampled on by men that I was born into this world. It was to share men's pain that I carried My cross." )
After reading the book, at first I didn't know what to make of this. By this point, we readers (or viewers) are worn out along with Rodrigues. Our powers of reasoning are blunted. Is there some untruth mixed in? Some lie? Or would Jesus have said the same?
What about the scripture that says, "If we deny Him, He also will deny us"? 
I believe that there is grace with God. He will forgive one denial, or three. He forgave Peter, after all.
But would He forgive Kichijiro? How many is too many?
...and yet Kichijiro followed Rodrigues "to the ends of the earth", so to speak. I see real hunger there. Truth, in the midst of weakness.
I agree with one thing: there is no "strong" or "weak". "Strong" people have simply not been tested to their limits. We are all weak, and would likely all apostatize except for God's sustaining grace.
So, where is accountability? Where is the line drawn? Where is the point of no return? Does that point only exist in human imagination, but not in God's reality? I don't think so, not based on that "deny" verse from 2 Timothy 2.
These are haunting questions.
I think the key here is repentance. Remember: Peter "wept bitterly". 
Denial is not unforgivable, but continual denial with no repentance will land us in a position where we also are denied by Jesus to the Father. Peter denied Jesus, but later went on to die for Him.
Let's go back to the fumie. ("Trample! Trample! I more than anyone know of the pain in your foot. Trample! It was to be trampled on by men that I was born into this world. It was to share men's pain that I carried My cross." )
Again, we must examine the base reasoning of these statements, just as we examined the reason for why someone might become a missionary in the first place.
Did Jesus come to share our pain? Or did He come to obliterate it?
Did he come to be trampled on by men, or did He come to trample death and sin?
Did He carry His cross with His eyes fixed on the present, or on eternity?
The question is not whether to save the few who are suffering now; it is whether to endanger the spiritual welfare of those who don't know Christ, and who are at risk of suffering for eternity!
It is not whether to share in pain, but whether to deny pain's hold over us. We are ALREADY VICTORIOUS.
The words that the fumie spoke were false. They sounded good at first, but we (along with Rodrigues) were worn out by circumstances. Only when we step back and reexamine First Principles do we see the error. May God in His grace sustain us to see the lies thrust at us by the evil one, and enable us to cling to Him.
 Shusaku Endo, Silence, p. 171.
 2 Timothy 2:12.
 Luke 22:62.